A SHORT COURSE IN THE MODELING OF CHEMOTAXIS

More documents

Recommendations

Info

Figure 4.1: Cartoon of the process of tumor induced angiogenesis. 39
the review [17] and the references therein). In this section, I will discuss the model of Levine, Sleeman, and Hamilton given in [16]. In their 2001 paper Mathematical Modeling of the Onset of Capillary Formation Initiating Angiogenesis, they offer a model of the first two stages of angiogenesis that captures the bimodal migration of endothelial cells (the formation of a tube structure). Levine et al. base their model on the interactions between one cellular species (ECs), four chemical species, and the receptors on the ECs. These are denoted by v The concentration of TAFs. c The concentration of proteolytic enzymes (MMPs). r The density of receptors to TAFs on the ECs. l The concentration of an intermediate receptor complex. η The density of ECs. and f The density of fibronectin. The model is then based on the following assumptions: (i) A TAF (v) bonds with a receptor (r) to form the intermediate complex (l). v + r (ii) The complex l induces the production of a new receptor and an MMP. l k1 ⇋ k−1 l k2 −→ c + r 40
Page 1 and 2: A SHORT COURSE IN THE MODELING OF C
Page 3 and 4: Contents List of Figures iii 1 Intr
Page 5 and 6: List of Figures 1.1 Life Cycle of D
Page 7 and 8: mobile species.” Referring back t
Page 9 and 10: this new form, as a plasmoid, the i
Page 11 and 12: the macroscopic (see Patlak [20]),
Page 13 and 14: η(x, t) The concentration of acras
Page 15 and 16: The only way for this result to hol
Page 17 and 18: Equation (2.2) is the identifying e
Page 19 and 20: 2.2 The Keller-Segel Model of Chemo
Page 21 and 22: Figure 2.1: The experimental config
Page 23 and 24: , b ′ → 0 and s → s0 as z →
Page 25 and 26: 2.4 Some conclusions In this chapte
Page 27 and 28: Chapter 3 Modeling: The Microscopic
Page 29 and 30: master equation of our pdf we need
Page 31 and 32: This equation assumes that our walk
Page 33 and 34: A number of observations can be mad
Page 35 and 36: The notable characteristic of this
Page 37 and 38: efore, the corresponding continuous
Page 39 and 40: or in two or more dimensions 34 ∂
Page 41 and 42: Chapter 4 Applications of the Kelle
Page 43: (SMCs). The ECs are the main cellul
Page 47 and 48: The first two assumptions immediate
Page 49 and 50: arrive at the system of interest
Page 51 and 52: 1/40 th of an hour, and during this
Page 53 and 54: Figure 4.3: Time evolution of the e
Page 55 and 56: Figure 4.5: Evolution of the growth
Page 57 and 58: tree. More advanced atherosclerotic
Page 59 and 60: three distinctive layers-the intima
Page 61 and 62: to be characterized by a change in
Page 63 and 64: eaction with a free radical R at a
Page 65 and 66: Lesion progression Smooth muscle ce
Page 67 and 68: Modeling Assumptions We begin by id
Page 69 and 70: gradient. For the immune cells and
Page 71 and 72: Both production and consumption app
Page 73 and 74: assume that the threshold values of
Page 75 and 76: The system (4.22)-(4.24) was solved
Page 77 and 78: Bibliography [1] E. De Angelis and
Page 79 and 80: [15] I. R. Lapidus, ”Pseudochemot
Page 81 and 82: Appendix A Linear Chemical Reaction
Page 83 and 84: proportional to A”. So that there
Page 85 and 86: Appendix B Bachmann-Landau Order Sy
Page 87: 3. Let h(τ) = e −τ and p(τ) =

A SHORT COURSE IN THE MODELING OF CHEMOTAXIS

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?